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Is light a wave or a particle? Yes!
Is the electron here or there? Yes!
Do physicists really know what they're talking about? Yes!

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We are introduced to the nature of Flatland by the narrator, a nameless Square, who describes his world as being populated primarily by regular polygons. A citizen's social and occupational status is in direct proportion to his number of sides, so those with so many sides that they approximate circles achieve the highest ranks. These circular elite are dubbed "priests" and rule Flatland apparently on a parliamentary model. At the other end of the spectrum are the Triangles, who constitute the working class. Even lower than the Triangles, however, are the simpleminded Lines -- and these are Flatland's women, useful only for procreation. It takes little imagination to guess what the irregular polygons represent.
The Square's purpose in writing this report is to rejoice in his discovery of the (previously unimagined) third dimension, revealed to him by a helpful Sphere who visits from Spaceland. The Square, now in possession of arcane knowledge and an intuitive conviction of the existence of higher dimensions, assumes an evangelical role and ultimately emerges as a Promethean figure when he is imprisoned for the heretical act of preaching a third dimension.
"Flatland" has been compared to "Alice in Wonderland" and "Gulliver's Travels," but I'd say there are clearer parallels to Huxley's "Brave New World" (in the classist regimentation of the Flatlanders' society) and Samuel Butler's "Erewhon" (in the Flatlanders' strange and limited belief system). The difference is that the aforementioned novels employ both irony to qualify as allegorical satires and narrative integrity to endure as pure fiction, whereas "Flatland" is so earnest in its delivery and so ineffectual in its impact, it feels like a pebble in an avalanche. Too obvious and elementary to be a scientific or mathematical essay, too obtuse to be a philosophical treatise, too moralistic to be a good example of a novel, "Flatland" misses its mark and slips silently through the cracks.

Flatland was written in a time before computers, and when "higher dimensions" were still about space and perception and analogy rather than some strange physics notion that this mathematette doesn't understand. It was also written in a time when it was appropriate for the author to have one-dimensional women in a two-dimensional world (or, alternatively, women as points in the one-dimensional world). This difference between the author's perspective and ours certainly adds a... "new dimension" to reading it!
I first read this book when I was 12 years old, and it was not at all above my head at that age. I'm no a professional mathematician, and I still enjoy reading the novel. I recommend it to anyone.

There is some amusing stuff here; the author is apparently a misogynist --women in Flatland are needle-thin, (well, that's not all bad) stupid, because of the size of their pointy heads (hey!) and violently dangerous due to their shape and lack of higher reasoning power.
Despite poking fun at females, this book is amusing and valuable since it can teach some great math prinicples. There is a "sequel" Sphereland published in the 20th century by a different author, that goes into dimensions higher than 3. It's fun, too. As an explanantion of the concept of dimension, plus for imagination, Flatland is a real classic and a favorite of mine.

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I am aware that Einstein had a certain philosophy regarding the correct way to write a biography, but this book was extremely dry. I was constantly reminded that I'm reading this for a physics class. Zzzz.....


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Hoffman wrote this book as if he is speaking directly to you, with a sense of humor and wit.
Are physicist right-well, most of the time.